The YouTube video suggests that to clean your bike helmet straps, you'll need to remove the pads (generally a gentle pull on the velcro to loosen them off) and hand washing is probably the easiest way. Since the straps themselves are not explicitly mentioned in this short excerpt, we can assume the pads that may be integrated into the straps can be cleaned by gentle handwashing after removing them.
More information would be needed to fully answer the question.